MATH 107 FINAL EXAMINATION SUMMER 2020

College Algebra MATH 107

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MATH 107 FINAL EXAMINATION

This is an open-book exam. You may refer to your text and other course materials as you work

on the exam, and you may use a calculator. You must complete the exam individually.

Neither collaboration nor consultation with others is allowed.

Record your answers and work on the separate answer sheet provided.

There are 30 problems.

Problems #1–12 are Multiple Choice.

Problems #13–21 are Short Answer. (Work not required to be shown)

Problems #22–30 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Determine the domain and range of the piecewise function

2. Solve: 11+ 2x = x − 2

3. Determine the interval(s) on which the function is increasing.

4. Determine whether the graph of y = 9+ x is symmetric with respect to the origin,

the x-axis, or the y-axis.

5. Solve, and express the answer in interval notation: | 5 – 6x | £ 13.

6. Which of the following represents the graph of 2x − 7y = 14 ?

7. Write a slope-intercept equation for a line parallel to the line x – 4y = 6 which passes through

the point (–8, 3).

8. Which of the following best describes the graph?

9. Express as an equivalent expression: 3 log y + log 1 – log (x + 2)

10. Which of the functions corresponds to the graph?

11. Suppose that a function f has no x-intercepts. Which of the following statements MUST be true?

12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No

formulas are given.) What is the relationship between g(x) and f (x)?

13. Multiply and simplify: (8 + 3i)(2 + 5i). Write the answer in the form a + bi, where a and b are real numbers

14. Solve, and write the answer in interval notation:

15. A can of soda at 82° F. is placed in a refrigerator that maintains a constant temperature of 35°

F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by

T(t) = 35 + 47 e  – 0.058 t       Find the temperature of the soda 10 minutes after it is placed in the refrigerator. (Round to the

nearest tenth of a degree.)

16. Find the value of the logarithm

SHORT ANSWER, with work required to be shown, as indicated.

22. Let f (x) = x + 3 and g (x) = x – 5.

(a) Find ) . Show work.

(b) Find the domain of the quotient function

g

f

. Explain.

24. Find the equation for a line which passes through the points (5, 2) and (8, –7). Write the

equation in slope-intercept form. Show work.

25. A salesperson earns a base salary of $1,475 per month and a commission of 8.4% on the

amount of sales. If the salesperson has a paycheck of $4,637.60 for one month, what was the

amount of sales for the month? Show work.

26. Let f (x) = 5x2 – 4 and g(x) = x – 2.

(a) Find the composite function ( f o g)(x) and simplify. Show work.

(b) Find ( f o g ) (−2) . Show work.

27. Find the exact solutions and simplify as much as possible: 8x2 = 6x + 1. Show work.

28. Given the function

1

( ) 4

7

f x = − x , find a formula for the inverse function. Show work.

Summer, 2020

23. Points (2, 1) and (6, –5) are endpoints of a line segment.

(a) What is the length of the line segment? Give the exact answer, no decimals, simplified as

much as possible. Show work.

(b) What is the midpoint M of the line segment?

Both parts of this problem are asking for composition

or evaluation of functions, not multiplication.

(c) Given the point M you found in part (b), state the point symmetric to M about the y-axis.

Do not multiply here. Evaluate the quotient function.

College Algebra MATH 107